A vertical well with a wellbore radius of $0\mathrm{.}4$ ft has been completed through the top half of the pay

zone. The pay zone is $80$ ft thick. The perforation density is $2$ shots$/$ft and the perforations are $6$

in$.$ long, resulting in a perforation skin factor, not considering any damage or other effects, of $6($sp

$=6).$ There also exists a damage zone around the well extending one foot into the formation from

the wellbore, in which the permeability is $10\%$ of the undamaged permeability.

a$.$ What is the total skin factor for this well?

b$.$ If the well is reperforated, adding the same type of perforations $(2$ spf$,6$ in$.-$long perforations$)$

along the remaining $40$ ft of reservoir zone $($fully completed$),$ what is the new total skin factor?

c$.$ If the well is originally perforated in the same zone $($top half of the pay zone$)$ to $2$ shots$/$ft and

$1\mathrm{.}5$ ft long, resulting in a perforation skin of $1,$ what is the total skin?